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            SMAC - Algorithm Specification
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<p>Algorithm Specification
    of the science processors of the MERIS/(A)ATSR Toolbox

<h3>SMAC</h3>

<p>SMAC is a <b>S</b>implified
    <b>M</b>ethod for <b>A</b>tmospheric <b>C</b>orrections of satellite measurements.
    It is a semi-empirical approximation of the radiative transfer in the atmosphere.
    The signal at the satellite is written as the sum of the following components,
    which are then expressed in simple analytical terms: </p>
<ul>
    <li>Two way gaseous transmission</li>
    <li>Atmospheric spherical
        albedo
    </li>
    <li>Total atmospheric transmission</li>
    <li>Rayleigh scattering</li>
    <li>Aerosol scattering</li>
</ul>

<p>To give an example, the
    spherical albedo, S, is expressed as a function of the aerosol optical depth
    at 550nm:</p>

<p><img src="images/SmacEquation.png"></p>

<p>where a<sub><font size="2">0</font></sub>
    and a<sub><font size="2">1</font></sub> are parameters which need to be determined
    for a given spectral band and aerosol model. These parameters can be retrieved
    by a best-fit against a full radiative transfer model. The well establish 6S
    code was used for this purpose.</p>

<p>With this technique the
    radiative transfer in the atmosphere can be computed much faster than with a
    full model. A comparison has shown that the gain in computation time is several
    hundred times in comparison with the full model (see reference below. Here the
    comparison was made with the predecessor 5S). However, numerous coefficients
    have to be determined in advance from best-fits with a full numerical model.
    Also, changes in the spectral band characteristics require new coefficients.
    The accuracy of the SMAC approximation in comparison with 5S is generally better
    than 3% difference between the TOA reflectances.</p>

<p>The practical application
    of such a simplified model is to invert the radiative transfer equation, and
    to calculate the surface reflectance from satellite measurements. Because of
    its "speed", this method is best suited for application to large data volumes.</p>

<p>The SMAC requires as input,
    in addition to the measured top of atmosphere radiances, the surface pressure,
    the ozone content and the water vapour content, and, most important, the aerosols.
    SMAC has also implemented these in a very useful way. Aerosol, for example,
    requires the selection of an aerosol model and the aerosol optical depth at
    550nm. The SNAP implementation gives the user the choice to select the MERIS
    meteorological data for pressure, ozone and humidity.</p>

<p>The algorithm is described
    in "SMAC : a simplified method for the atmospheric correction of satellite measurements
    in the solar spectrum" H. RAHMAN, G. DEDIEU Int. J. Remote Sensing, 1994, vol.15,
    no.1, 123-143.</p>
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